The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X  0  0  X  0  X a*X  X  X a*X a*X a*X a^2*X  X  0 a^2*X  0 a^2*X  X a^2*X a^2*X a^2*X  X  X  X  X  0 a*X  0  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X  0 a*X a^2*X  X a^2*X a*X  X a^2*X  0  X  X  X  0  X  0 a*X a^2*X  X  X  X  X  0  X a*X a*X  X  0  X a*X  X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  0  X a^2*X  X a^2*X a^2*X a*X  0 a^2*X  X a*X a^2*X a^2*X a^2*X  X a^2*X a*X  0 a*X a*X  X a^2*X  X a^2*X  X  X a^2*X a^2*X a^2*X  X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X a*X  0 a^2*X a*X a*X  X a*X a*X a^2*X  X  0  X a*X  0 a*X a*X  X a*X a*X  0 a*X a^2*X  0 a*X a^2*X  X  X a^2*X a^2*X a*X

generates a code of length 46 over F4[X]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+93x^124+189x^128+192x^130+162x^132+576x^134+150x^136+1344x^138+108x^140+960x^142+102x^144+60x^148+57x^152+27x^156+33x^160+30x^164+9x^168+3x^176

The gray image is a linear code over GF(4) with n=184, k=6 and d=124.
This code was found by Heurico 1.16 in 0.136 seconds.